Theorems · Theorem · group theory
Submonoid.isLocalizationMap_iff_bijective
∀ {M : Type u_1} {G : Type u_2} {F : Type u_3} [inst : CommMonoid M] [inst_1 : CommGroup G] {S : Submonoid G}
[inst_2 : FunLike F G M] [MulHomClass F G M] {f : F}, S.IsLocalizationMap ⇑f ↔ Function.Bijective ⇑f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- mul_oneproof · cited by 3,885
- Submonoidstatement and proof · cited by 3,086
- FunLikestatement and proof · cited by 2,560
- CommMonoidstatement and proof · cited by 2,264
- mul_assocproof · cited by 1,667
- MulEquivproof · cited by 1,142
- map_mulproof · cited by 1,137
- CommGroupstatement and proof · cited by 990
- Function.Bijectivestatement and proof · cited by 863
- div_eq_mul_invproof · cited by 715
- mul_inv_cancelproof · cited by 128
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.isLocalizationMap_idproof · cited by 0